Nancy and Mark commute to work, traveling in opposite directions. Nancy leaves the house at 7 :00 A. M. and averages 15 miles per hour. Mark leaves at 7 :15 A. M. and averages 60 miles per hour. At what time will they be 135 miles apart?

At time 9 : 00 AM they are 135 miles apart.

Step-by-step explanation:

Nancy leaves the house at 7 :00 A. M. and averages 15 miles per hour. Mark leaves at 7 :15 A. M. and averages 60 miles per hour.

Let the time after the start of Mark when they are 135 miles apart be t hours.

Time traveled by Nancy = t + 7:15 - 7:00 = t + 15 minutes = (t+0.25) hours

They are traveling in the opposite direction so,

Distance between them = Speed of Nancy x Time of travel of Nancy + Speed of Nancy x Time of travel of Nancy

135 = 15 x (t+0.25) + 60 x t

135 = 15t + 3.75 + 60t

75t = 131.25

t = 1.75 hours = 1 hour 45 minutes

Time = 7: 15 + 1 hour 45 minutes = 9 : 00 AM

At time 9 : 00 AM they are 135 miles apart.